# arctan proc

Source: https://ref.dm-lang.org/proc/arctan
Added in BYOND 513.

### Format
- `arctan(Num)`
- `arctan(x, y)`
- `arctan(Vector)`


### Args
- `Num`: A number
- `x, y`: 2D coordinates
- `Vector`: A vector (only 2 dimensions are used)


### Returns
> The inverse tangent in degrees.

When `arctan` is called with just one number argument, the number is a tangent, and the return value is the angle that produces that tangent. The resulting angle can range from -90 to 90.

The two-argument form returns a polar angle from -180 to 180. This angle starts at 0° for due east, and increases counter-clockwise from there. Therefore 1,0 has an arctangent of 0°, 0,1 is 90°, -1,0 is 180°, and so on. At point 0,0 the angle is undefined since it could be any angle, but `arctan` will return 0.

Finally, you can use a vector instead of a number. Only the x and y components of a vector will be used.

```dm /arctan/
mob/verb/test()
   usr << arctan(0)        // 0
   usr << arctan(1)        // 45
   usr << arctan(sqrt(3))  // 60

   // polar coordinates
   usr << arctan(3, 4)     // 53.1301
   usr << arctan(-1, 1)    // 135
   usr << arctan(0, -5)    // -90
```

Here's another example, in which a rotating turret points to a target on another tile.

```dm /arctan/
mob/turret
   proc/PointAt(atom/target)
      if(!target) return
      var/dx = target.x - x
      var/dy = target.y - y
      // turret's icon normally faces east
      transform = matrix().Turn(-arctan(dx, dy))
```

### See also
- [arcsin proc](https://ref.dm-lang.org/proc/arcsin.md)
- [arccos proc](https://ref.dm-lang.org/proc/arccos.md)
- [tan proc](https://ref.dm-lang.org/proc/tan.md)
- [turn proc](https://ref.dm-lang.org/proc/turn/index.md)